Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

learn more… | top users | synonyms (2)

2
votes
1answer
56 views

What's the numerator and the denominator of a fraction called?

Just a quick question, is it right to call the numerator and the denominator of a fraction by "terms"? I don't think that "terms" is the right word here, but i don't know any alternatives. Can any ...
1
vote
2answers
37 views

Is there an adjective to describe systems of equations which is neither underdetermined nor overdetermined?

What might I call a system of equations in which the number of equations equals the number of free variables? In other words, if a system of equations is neither underdetermined nor overdetermined, ...
0
votes
0answers
8 views

What is the term for a general set of objects whose higher dimensional analogs have hyper- in front of them?

Strange terminology question: we tend to name things in low dimensional space and then generalize after a certain point. For instance, we have point, line, plane, and then hyperplane (there is no 4 ...
1
vote
1answer
27 views

What is a polynomial with infinite number of terms?

My instructor commented that a structure function $\phi(G)$ of a graph is a polynomial if a finite number of terms. So what is the thing with infinite number of terms? Why not polynomial?
0
votes
0answers
6 views

Set intersection with margin: terminology

I implemented an algorithm that calculates the intersection of two sets with a certain margin and returns the matched tuples: Let A, B be sets. $C = \{ (a \in A, b \in B) | lowerbound <= a - b &...
1
vote
1answer
21 views

Properties of Infinite set on co-finite topology and Countable set on co-countable topology

I am trying to verify some of the properties of infinite set on co-finite topology and countable set on co-countable topology but it is proven to be very tricky because I cannot visualize the spaces. ...
2
votes
1answer
76 views

Are there any “default” properties which hold for almost all topological spaces in analysis?

What is the simplest/most general commonly used (type of) topological space in analysis? For instance, every example I can think of in analysis is first-countable. I don't think it can be metric ...
2
votes
0answers
32 views
+50

Is the infinitesimal generator for Lie groups the same as the infinitesimal generator of a Markov semigroup?

Is the infinitesimal generator for Lie groups related to the infinitesimal generator of a Markov semigroup? Or are they totally different concepts? https://en.wikipedia.org/wiki/Lie_group#...
2
votes
0answers
16 views

Is there a name for the relation of a directed set?

If $(X,R)$ is an ordered set then we say $R$ is an order in $X$, how do we call the relation $R$ if $(X,R)$ is a directed set? A direction in X?
3
votes
0answers
53 views

Is there a name for a topological space $X$ in which every proper closed subset is compact? [duplicate]

Is there a name for a topological space $X$ in which every proper closed subset is compact$^{(*)}$? It is well known that in a compact topological space, every closed set is compact. Hence, the class ...
1
vote
0answers
18 views

Help understanding proof of Frostman's Lemma - issue technical or termonological?

I was reading Hochman's proof of Frostman's lemma in his online lecture notes here and got hung up. I'm not sure if I'm missing a part of the proof or I'm misunderstanding the theorem itself. The ...
1
vote
2answers
38 views

Is this the correct definiton of $T_1$ space?

I found this in a handwritten note: Def: A topological space $X$ is $T_1$ if $\forall x \neq y \in X$ there exist a neighborhood of $y$ such that s.t. $x \not\in V$. I was almost certain that ...
0
votes
0answers
24 views

Why is the typewriter sequence named as such?

I refer to the typewriter sequence (see https://terrytao.wordpress.com/2010/10/02/245a-notes-4-modes-of-convergence/) defined by: $$f_n := {\mathbb 1}_{\left[\dfrac{n-2^k}{2^k},\dfrac{n-2^k+1}{2^k}\...
12
votes
2answers
306 views

Can Path Connectedness be Defined without Using the Unit Interval?

Can path connectedness be defined without using the unit interval or more generally the real numbers? I.e., do we need Dedekind cuts or Cauchy convergence equivalence classes of the rational ...
0
votes
0answers
37 views

What does “factoring out an (group) action $\tau$ of a group $G$ acting on some set $E$” mean?

I am reading a survey article where they define the following objects: $\Gamma:=\mathbb{Z}^{n}$ seen as a group of translations. $\mathbb{T}:=\mathbb{R}^{n}/\Gamma$ is the $n$-dimensional ...
1
vote
1answer
35 views

inverse limit as a functor

I have a question about inverse limits based on https://en.wikipedia.org/wiki/Inverse_limit . In the section "general definition" there is noted that an inverse system is a contravariant functor $I\...
0
votes
1answer
24 views

What's the definition of being zero to infinite order at some point?

I'm reading a paper and it says The differential form $\psi$ is zero to infinite order at all points of $F$.That is,all coefficients of $\psi$ are zero to infinite order at points of $F$.(Here $\psi$...
1
vote
1answer
57 views

Can someone reconcile the two definition of Suslin's condition?

I am given two definitions of the so called "Suslin's condition" and I need to reconcile them. I am an undergrad and this is just for exploration. Definition 1. A partially ordered set $X$ is said ...
0
votes
2answers
63 views

what do curly brackets mean in this number theory equation?

$$(\lfloor y\rfloor-1)(\lfloor x\rfloor-1)=\{x\}+\{y\}+1$$ From looking at the LaTeX, I can see the left-hand side symbols mean the floor of the variable, but the right-hand side doesn't give much ...
0
votes
2answers
123 views

When are quantities outside of the real numbers considered equal, and when do they exist?

I know of the complex number $i$ and it's existence as the result of invalid square rooting (the square root of negative one does not exist inside the real numbers), but other than complex numbers, ...
0
votes
1answer
36 views

Topology: What is a quick way to check whether a subset $D$ is dense in $(X, \mathcal{T})$?

Def $1$: Let $(X, \mathcal{T})$ be a topological space, then $D \subseteq X$ is dense if $\overline {D} = X$ Def $2$: $x \in \overline D$ iff for all $U \in \mathcal{T}, x \in U \implies D \cap U \...
2
votes
1answer
38 views

Name of the distribution with density $P(x) e^{-x/\theta}$, where $P$ is a polynomial with positive coefficients.

The Gamma distribution of shape $k$ and scale $\theta$ has density $\frac1{\Gamma(k)\theta(k)} x^{k-1} e^{-x/\theta}$. Consider the more general distribution with density (up to a normalizing constant)...
0
votes
0answers
49 views

Covering maps of schemes.

A curve $X$ is modular if there is a finite covering $X_0(N)\rightarrow X$. What does covering mean in this context, and for more general morphisms of schemes? Just covering as topological spaces?
0
votes
0answers
12 views

Quasi-Isomorphism of Sheaf complexes terminology

Let $F$ and $G$ be sheaves of $R$-modules over a topological space $X$. Suppose we have isomorphisms $H^i(F)\simeq H^i(G)$ for all $i\in\mathbb{N}$. What is the proper term for this? Can one just say ...
1
vote
1answer
39 views

Complementarity and Substitutability

I am reading a paper in the international journal of game theory entitled Unequal Connections by Goyal and Joshi (2006) and it has the following sentences: "If strategic complementarity obtains... In ...
1
vote
1answer
28 views

Proposition about rings of fractions

This is taken from Atiyah-Macdonald's Commutative algebra book page 41. Someone please explain to me what is the meaning of "$a$ meets $S$". This is the first time I'm seeing this in the book.
0
votes
1answer
47 views

Are there any examples of consistent proper axiomatic extensions of classical logic?

By a proper axiomatic extension, I mean a logic with the same set of well formed formulas as classical logic, but with the set of theorems of the logic a proper superset of the theorems of classical ...
0
votes
2answers
76 views

What is the difference between Definite Integral & Indefinite Integral on the basis of their connection with derivatives?

I'm reading Denlinger's text on Real Analysis.There is a difference mentioned b/w definite integrals and indefinite integrals as-"The definite integral is a fundamentally significant concept,existing ...
1
vote
0answers
24 views

On a stronger property than being an Armendariz ring

A ring $R$ is said to be Armendariz if $f(x), g(x) \in R[x]$ are such that $f(x)g(x) = 0$, where $f(x) = a_nx^n + \dots a_0, g(x) = b_mx^m + \dots + b_0$, then $a_ib_j=0$ for all $i,j$. In other ...
1
vote
1answer
57 views

What does “pcr” stand for?

For example, as shown in this OEIS page: $P(n,4)=\frac{2n^3+6n^2-9n-13+(9n+9)\text{pcr}\{1,-1\}(2,n)-32\text{pcr}\{1,-1,0\}(3,n)-36\text{pcr}\{1,0,-1,0\}(4,n)}{288}$
1
vote
0answers
21 views

Are these correct extension of injective and surjective functions?

Recall the definition of injective and surjective functions: 1.a A function $f: X \to Y$, is injective if for all $a,b \in X$, if $a \neq b$, then $f(a) \neq f(b)$ 1.b A function $f: X \to Y$,...
1
vote
0answers
20 views

Subgraph with “dangling edges”?

I was wondering if there is a notion in graph theory where one can have a subgraph such that the endpoints of all of the edges in the subgraph are not necessarily included in the vertex set of the ...
1
vote
2answers
31 views

Is Reliability Component a vertex?

The term component has a distinct definition in graph theory from vertex while the terms components and vertices can be mostly the same in Realiability Engineering, my intuition. So how is the term ...
0
votes
0answers
39 views

Does the “Leibniz multicategory over $R$” have an accepted name?

Let $R$ denote a commutative ring. Definition. The "Leibniz multicategory" over $R$ is given as follows: Objects. $R[D]$-modules (where $D$ is a formal symbol; an 'indeterminate'). ...
1
vote
1answer
58 views

How to predict the incidents of synchronization for multiple oscillations.

EDIT: I changed the title of this question and made this edit based on a conversation with a friend. While I am dealing with mechanical cams the plain fact is that what I have is an oscillation in ...
1
vote
2answers
38 views

What does the condition of $T_{3\frac{1}{2}}$ space mean exactly?

A topological space $(X,\mathcal{T})$ is said to be $T_{3\frac{1}{2}}$ if given $x \in X$, and a closed set $C \subset X$, $x \not \in C, \exists f:X \to [0,1]$ s.t. $f(x) = 0, f(C) = 1$ This ...
2
votes
4answers
235 views

Is $3+2=5$ a equation?

Problem: Is $3+2=5$ a equation ? Solution As we know that that $3+2$ is a arithmetic expression. So $3+2 = 5$ is a arithmetic equation. But my friend said that $3+2=5$ is not a equation as it ...
0
votes
1answer
15 views

Direct proportional - basic concept

Q : A stone is dropped from the top of a high tower. The distance it falls is proportional to the square of the time of fall. The stone falls 19.6 m after 2 seconds, how far does it fall after 3 ...
1
vote
1answer
26 views

Term for sum, difference, product, quotient

Feel free to let me know if this is better suited for: https://english.stackexchange.com/ https://stackoverflow.com/ That said, I'm wondering if there's a math term for the nature of "sum", "...
0
votes
0answers
12 views

What is name of structures composed of a domain set, a function and a range set?

What is name of structures composed of a domain set, a function and a range set? Are such structures fall under a subject besides set theory or function theory?
1
vote
1answer
33 views

What are “irreducible factors” in a field?

I am really not understanding what "irreducible factor" in $F[X]$ for field $F$ means. can someone explain? for example is $(x - 1)^2$ irreducible? in my current understanding I think yes. but I ...
0
votes
1answer
58 views

A term for a function $f$ such that $x f'(x)$ is decreasing

Consider a differentiable, monotonically increasing function $f$. If $f'(x)$ is increasing, then $f$ is convex. If $f'(x)$ is decreasing, then $f$ is concave. Is there a term that describes $f$ when ...
0
votes
1answer
43 views

Are matrices 2D by definition?

On the one hand, I read on Wikipedia that [A] matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. However, googling "3D matrix" ...
1
vote
1answer
32 views

What is the proper notation for vectors that uses only integers? $\Bbb Z^n$?

How do I denote vectors, similar to $\Bbb R^n$ but with integers instead of the reals? Just $\Bbb Z^n$? Would vectors of exclusively positive integers be $\Bbb Z^{{+n}}$ then? (since $\Bbb Z^+$)
0
votes
0answers
9 views

Name for a “pseudo-diagonally dominant matrix”

I'm doing a literature search, and I'm just wondering if there is a name for (Hermitian positive definite) matrices which have the sum of the off-diagonals in any given row dominated by the diagonal ...
0
votes
0answers
34 views

Is there a term for the dimension of the annihilator of an element of an algebra?

Let $\mathcal{A}$ be a finite dimensional $R$-algebra, and for $x \in \mathcal{A}$ consider $\mathrm{Ann}(x) = \{ c \in \mathcal{A} \mid cx = 0 \}$. Is there a term for the dimension of this subspace? ...
0
votes
0answers
39 views

Alternative view of matrix inversion (explanation required)

We were taught in linear algebra that in order to try to find the inverse of a matrix we can create an augmented matrix $[AI]$ where $A$ is the original matrix and $I$ is the identity matrix. Then we ...
1
vote
1answer
62 views

What does it mean for an automorphism to centralize factor group $G/M$?

Let $G$ be a group and $M$ be a normal subgroup of it. An automorphism $\phi$ centralizes the factor group $G/M$. What does it mean for an automorphism to centralize a factor group $G/M$? I ...
1
vote
3answers
46 views

Are scalars a synonym for the elements of $\mathbb R^1$?

Are scalars a synonym for the elements of $\mathbb R^1$, or is there a subtle difference?
1
vote
1answer
48 views

Terminology: is it random?

The topic of research of my master thesis is the use of probabilistic methods and models in music composition, particularly in the field of algorithmic music. As often is the case, artists tend to be ...